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Nonlinear Buckling and Postbuckling Response of Porous FGM Shallow Spherical Caps and Circular Plates with Nonlinear Elastic Foundation Effects Using the Ritz Energy Method

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Mechanics of Composite Materials Aims and scope

A new analytical study for nonlinear buckling and postbuckling behavior of porous functionally graded material (FGM) circular plates and shallow spherical caps resting on nonlinear elastic foundation was carried put using the nonlinear Reddy’s higher-order shear deformation theory (HSDT). The spherical caps/circular plates under thermo-mechanical loadings were considered, and the nonlinear elastic foundation was used to model the behavior of hardening and softening foundations. The total potential energy expressions of caps/plates were established, and the Ritz energy method was applied. The analytical expressions of load-deflection relationships were obtained. The critical buckling loads and postbuckling behavior of shells/plates were determined and analyzed. The remarkable influences of geometrical parameters, material parameters, and nonlinear foundation stiffnesses on the nonlinear static stability behavior of caps and circular plates were noted.

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References

  1. M. Lan, W. Yang, X. Liang, S. Hu, and S. Shen, “Vibration modes of flexoelectric circular plate,” Acta Mech. Sin., 38, 422063 (2022).

    Article  Google Scholar 

  2. D. Haojiang, X. Rongqiao and C. Weiqui, “Exact solutions for free vibration of transversely isotropic piezoelectric circular plates,” Acta Mech. Sin., 16, 141-147 (2000).

    Article  Google Scholar 

  3. T. C. Yuan, J. Yang, and L. Q. Chen, “Nonlinear vibration analysis of a circular composite plate harvester via harmonic balance,” Acta Mech. Sin., 35, 912-925 (2019).

    Article  Google Scholar 

  4. M. R. Eslami, H. R. Ghorbani, and M. Shakeri, “Thermoelastic buckling of thin spherical shells,” J. Therm. Stress., 24, No. 12, 1177-1198 (2001).

    Article  Google Scholar 

  5. E. I. Starovoitov and D. V. Leonenko, “Deformation of an elastoplastic three-layer circular plate in a temperature field,” Mech. Compos. Mater., 55, No. 4, 503-512 (2019).

    Article  Google Scholar 

  6. R. Shahsiah and M. R. Eslami, “Thermal and mechanical instability of an imperfect shallow spherical cap,” J. Therm. Stress., 26, No. 7, 723-737 (2003).

    Article  Google Scholar 

  7. J. Go, A. M. Afsar, and J. I. Song, “Analysis of thermoelastic characteristics of a rotating fgm circular disk by finite element method,” Adv. Compos. Mater., 19, No. 2, 197-213 (2010).

    Article  Google Scholar 

  8. N. D. Duc and H. V. Tung, “Mechanical and thermal postbuckling of shear-deformable FGM plates with temperature-dependent properties,” Mech. Compos. Mater., 46, No. 5, 461-476 (2010).

    Article  Google Scholar 

  9. A. H. Sofiyev and N. Kuruoglu, “Non-linear buckling of an FGM truncated conical shell surrounded by an elastic medium,” Int. J. Press.Vessels Pip., 107, 38-49 (2013).

    Article  Google Scholar 

  10. R. Saini, S. Saini, R. Lal, and I. V. Singh, “Buckling and vibrations of FGM circular plates in thermal environment,” Procedia Struct. Integr., 14, 362-374 (2019).

    Article  Google Scholar 

  11. F. Farhatnia, M. G. Mobarakeh, S. Rasouli, and S. Oveissi, “Thermal buckling analysis of functionally graded circular plate resting on the pasternak elastic foundation via the differential transform method,” Facta Universitatis, Series: Mech. Eng., 15, No. 3, 545-563 (2017).

    Google Scholar 

  12. E. Arshid, A. Kiani, S. Amir, and M. Z. Dehaghani,” Asymmetric free vibration analysis of first-order shear deformable functionally graded magneto-electro-thermo-elastic circular plates,” Proc. Inst. Mech. Eng. C. J. Mech. Eng. Sci., 233, No. 16, 5659-5675 (2019).

  13. Y. Kiani, “Axisymmetric static and dynamics snap-through phenomena in a thermally postbuckled temperature-dependent FGM circular plate,” Int. J. Non-Linear Mech., 89, 1-13 (2017).

    Article  Google Scholar 

  14. M. Jabbari, E. Shahryari, H. Haghighat, and M. R. Eslami, “An analytical solution for steady state three dimensional thermoelasticity of functionally graded circular plates due to axisymmetric loads,” Eur. J. Mech. A/Solids., 47, 124-142 (2014).

    Article  Google Scholar 

  15. J. R. Reddy, E. Ruocco, J. A. Loya, and A. M. A. Neves, “Theories and analyses of functionally graded circular plates,” Compos. Part C: Open Access., 5, 100166 (2021).

    Google Scholar 

  16. I. Eshraghi and S. Dag, “Forced vibrations of functionally graded annular and circular plates by domain-boundary element method,” Z. Angew. Math. Mech., 100, No. 8, 201900048 (2020).

  17. D. H. Bich, D. V. Dung, and L. K. Hoa, “Nonlinear static and dynamic buckling analysis of functionally graded shallow spherical shells including temperature effects,” Compos. Struct., 94, No. 9, 2952-2960 (2012).

    Article  Google Scholar 

  18. R. Shahsiah, M. R. Eslami, and R. Naj, “Thermal instability of functionally graded shallow spherical shell,” J. Therm. Stress., 29, No. 8, 771-790 (2006).

    Article  Google Scholar 

  19. M. S. Boroujerd and M. R. Eslami, “Nonlinear axisymmetric thermomechanical response of piezo-FGM shallow spherical shells,” Arch. Appl. Mech., 83, 1681-1693 (2013).

    Article  Google Scholar 

  20. M. S. Boroujerdy and M. R. Eslami, “Axisymmetric snap-through behavior of piezo-FGM shallow clamped spherical shells under thermo-electro-mechanical loading,” Int. J. Press. Vessel. Pip., 120-121, 19-26 (2014).

    Article  Google Scholar 

  21. M. S. Boroujerdy and M. R. Eslami, “Unsymmetrical Buckling of Piezo-FGM Shallow Clamped Spherical Shells under Thermal Loading,” J. Therm. Stress., 38, No. 11, 1290-1307 (2015).

    Article  Google Scholar 

  22. T. Prakash, M. K. Singha, and M. Ganapathi, “Nonlinear dynamic thermal buckling of functionally graded spherical caps”. AIAA J., 45, No. 2, 505-508 (2007).

    Article  Google Scholar 

  23. N. T. Phuong, V. H. Nam, and D. T. Dong, “Nonlinear vibration of functionally graded sandwich shallow spherical caps resting on elastic foundations by using first-order shear deformation theory in thermal environment,” J. Sandw. Struct. Mater., 22, No. 4 1157-1183 (2020).

    Article  Google Scholar 

  24. D. K. Sharma, J. N. Sharma, S. S. Dhaliwal, and V. Walia, “Vibration analysis of axisymmetric functionally graded viscothermoelastic spheres,” Acta Mech. Sin., 30, 100-111 (2014).

    Article  CAS  Google Scholar 

  25. L. N. Ly, D. T. N. Thu, D. T. Dong, V. M. Duc, B. T. Tu, N. T. Phuong, and V. H. Nam, “A novel analytical approach for nonlinear thermo-mechanical buckling of higher-order shear deformable porous circular plates and spherical caps with FGM face sheets,” Int. J. Appl. Mech., 15, No. 5, 2350035 (2023).

  26. J. H. Zhang, X. Liu, and X. Zhao, “Symplectic method-based analysis of axisymmetric dynamic thermal buckling of functionally graded circular plates,” Mech. Compos. Mater., 55, No. 4, 455-466 (2019).

    Article  Google Scholar 

  27. Y. Heydarpour, P. Malekzadeh, and F. Gholipour, “Thermoelastic analysis of FG-GPLRC spherical shells under thermomechanical loadings based on Lord-Shulman theory,” Compos. B. Eng., 164, 400-424 (2019).

    Article  CAS  Google Scholar 

  28. A. Eyvazian, F. Musharavati, P. Talebizadehsardari and T. A. Sebaey, “Free vibration of FG-GPLRC spherical shell on two parameter elastic foundation,” Steel Compos. Struct., 36, No. 6, 711-727 (2020).

    Google Scholar 

  29. M. Javani, Y. Kiani, and M. R. Eslami, “Geometrically nonlinear free vibration of FG-GPLRC circular plate on the nonlinear elastic foundation,” Compos. Struct., 261, 113515 (2021).

    Article  Google Scholar 

  30. D. Liu, Z. Zhou and J. Zhu, “On the free vibration and bending analysis of functionally graded nanocomposite spherical shells reinforced with graphene nanoplatelets: Three-dimensional elasticity solutions,” Eng. Struct., 226, 111376 (2021).

    Article  Google Scholar 

  31. N. T. Phuong, D. T. Dong, B. T. Tu, V. M. Duc, L. N. Khuong, P. T. Hieu, and V. H. Nam, “Nonlinear thermo-mechanical axisymmetric stability of FG-GPLRC spherical shells and circular plates resting on nonlinear elastic medium,” Ships Offshore Struct. Published online 22/05/2023, https://doi.org/10.1080/17445302.2023.2214489.

  32. C. Chu, M. S. H. Al-Furjan, R. Kolahchi, and A. Farrokhian, “A nonlinear Chebyshev-based collocation technique to frequency analysis of thermally pre/post-buckled third-order circular sandwich plates,” Commun. Nonlinear Sci. Numer., 118, 107056 (2023).

    Article  Google Scholar 

  33. P. Liu and T. He, “Dynamic analysis to the fractional order thermoelastic problem of porous structure,” Z. Angew. Math. Mech., 102, No. 9, 202100251 (2022).

  34. H. A. Atmane, A. Tounsi, and F. Bernard, “Fabrice effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations,” Int. J. Mech. Mater. Des., 13, No.1, 71-84, (2017).

    Article  Google Scholar 

  35. M. S. H. Al-Furjan, X. S. Kong, L. Shan, G. Soleimani Jafari, A. Farrokhian, X. Shen, R. Kolahchi and D. K. Rajak, “Influence of LPRE on the size-dependent phase velocity of sandwich beam including FG porous and smart nanocomposite layers,” Polym. Compos., 43, No.10, 7390 (2022).

  36. M. Amir and M. Talha, “Imperfection sensitivity in the vibration behavior of functionally graded arches by considering microstructural defects,” Proc. Inst. Mech. Eng. C. J. Mech. Eng. Sci., 233, No. 8, 2763-2777 (2018).

    Article  Google Scholar 

  37. H. Babaei and M. R. Eslami, “Study on nonlinear vibrations of temperature- and size-dependent FG porous arches on elastic foundation using nonlocal strain gradient theory,” Eur. Phys. J. Plus., 136, 24 (2021).

    Article  Google Scholar 

  38. M. R. Barati and A. M. Zenkour, “Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions,” J. Vib. Control., 24, No. 10, 1910-1926 (2016).

    Article  Google Scholar 

  39. A. Gupta and M. Talha, “Influence of porosity on the flexural and free vibration responses of functionally graded plates in thermal environment,” Int. J. Struct. Stab. Dyn., 18, No. 01, 1850013 (2018).

  40. V. H. Nam, N. T. Phuong, D. T. Dong, N. T. Trung, and N. V. Tue, “Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners,” Proc. Inst. Mech. Eng. C. J. Mech. Eng. Sci., 233, No. 17, 6177-6196 (2019).

    Article  Google Scholar 

  41. N. K. H. Shivaramaiah, S. Kattimani, M. Shariati, and N. T. Trung, “Geometrically nonlinear behavior of two-directional functionally graded porous plates with four different materials,” Proc. Inst. Mech. Eng. C. J. Mech. Eng. Sci., 236, No. 22, 11008-11023 (2022).

    Article  Google Scholar 

  42. Q. Li, S. Wang and J. Zhang, “Free vibration analysis of graded porouscircularmicro/ nanoplates with various boundary conditions based on the nonlocal elasticity theory,” Z. Angew. Math. Mech., 103, No. 02, 202200159 (2022).

  43. M. S. H. Al-Furjan, C. Yin, X. Shen, R. Kolahchi, M. S. Zarei, and M. H. Hajmohammad, “Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate”, Mech. Syst. Signal Process., 178, 109269 (2022).

    Article  Google Scholar 

  44. M. S. H. Al-Furjan, S. Fan, L. Shan, A. Farrokhian, X. Shen, and R. Kolahchi, “Wave propagation analysis of micro air vehicle wings with honeycomb core covered by porous FGM and nanocomposite magnetostrictive layers,” Waves Random Complex Media, (2023). DOI: https://doi.org/10.1080/17455030.2022.2164378

    Article  Google Scholar 

  45. M. Motezaker, M.Jamali, and R. Kolahchi, “Application of differential cubature method for nonlocal vibration, buckling and bending response of annular nanoplates integrated by piezoelectric layers based on surface-higher order nonlocalpiezoelasticity theory,” J. Comput. Appl. Math., 369, 112625 (2020).

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Transport Technology, University of Transport Technology, Hanoi, 10000, Vietnam

    Bui Tien Tu & Vu Minh Duc

  2. Faculty of Fundamental Science for Engineering, University of Transport Technology, Hanoi, 10000, Vietnam

    Bui Tien Tu

  3. Laboratory of Advanced Materials and Structures, Institute for Advanced Study in Technology, Ton Duc Thang University, Ho Chi Minh City, 70000, Vietnam

    Dang Thuy Dong

  4. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, 70000, Vietnam

    Dang Thuy Dong

  5. Faculty of Civil Engineering, University of Transport Technology, Hanoi, 10000, Vietnam

    Vu Hoai Nam

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Correspondence to Dang Thuy Dong.

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Tu, B.T., Dong, D.T., Duc, V.M. et al. Nonlinear Buckling and Postbuckling Response of Porous FGM Shallow Spherical Caps and Circular Plates with Nonlinear Elastic Foundation Effects Using the Ritz Energy Method. Mech Compos Mater 60, 417–432 (2024). https://doi.org/10.1007/s11029-024-10200-7

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  • DOI: https://doi.org/10.1007/s11029-024-10200-7

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